Quiz23solutions - MAC1105: Quiz #23 Solutions July 26, 2010...

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Unformatted text preview: MAC1105: Quiz #23 Solutions July 26, 2010 In the top-right corner of a clean sheet of paper, write your name, UFID, and section number. Please use a pen with blue or black ink. When you are nished, FOLD your paper in half lengthwise and write your name on the back. 1. Solve: 7 (a) 2x-3 = 23x+4 x - 3 = 3x + 4 -7 = 2x x = - 2 . (b) 3x 2. Solve: = 9x+3 3x -3x = 32(x+3) x2 - 3x = 2x + 6 x2 - 5x - 6 = 0 (x - 6)(x + 1) = 0 x = 6, -1. 2 -3x 2 (a) 2 ln(x + 1) = ln4 ln(x + 1)2 = ln 4 (x + 1)2 = 4 x2 + 2x + 1 = 4 x2 + 2x - 3 = 0 (x + 3)(x - 1) = 0 x = -3, 1, but we throw out x = -3. (b) log3 x + log3 (x + 2) = 1 log3 [x(x + 2)] = 1 x2 + 2x = 3 x2 + 2x - 3 = 0 x = -3, 1 (as above), but throw out x = -3. 3. The Census Bureau measured the population of a small town to be 1000 in the year 2000. This year, the Census counted 2,000 people in the town. If the town keeps growing at the same rate, how many people should there be in the year 2017? We use A1 = A0 ekt ; here A1 = 2000, A0 = 1000, t = 10, and we must solve for k. So we have the equation 2000 = 1000ek(10) 2 = e10k ln 2 ln 2 = 10k ln 2 = k . In 2017, t = 17, so we have A1 = 1000e 10 17 . 10 1 ...
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